Grid dome roof structure



Nov. 29, 1966 R. c. ULM

GRID DOME ROOF STRUCTURE 3 Sheets-Sheet 1 Filed April 22, 1964 INVENTOR.

64972 C JZHZ BY We $2 %//%M W 9, 1966 R. c. ULM 3,22%

GRID DOME ROOF STRUCTURE Filed April 22, 1964 5 Sheets-Sheet 2 INVENTOR.

NOV. 29, 1966 c, M 3,237,864

GRID DOME ROOF STRUCTURE Filed April 22, 1964 5 Sheets-Sheet 3 I MOMENT F I/VE/PT/A k c E Q K fi FAD/U5 0F ROOF //V F7.

INVENTOR. fie/gm 6. f/Zfi;

M, m PW- United States atent Jersey Filed Apr. 22, 1964, Ser. No. 361,837 14 Claims. (Cl. Z81) The present invention relates to dome structures. It deals more particularly with dome structures of the selfsupporting type.

Self-supporting domes presently find wide use a roofs for sports arenas, exposition buildings, and storage tanks and the like. Numerous structural arrangements have been devised for these domes; particularly with the advent of steel constructions. One such structural arrangement is a grid layout of arches, or generally parallel series of arches, extending perpendicular to each other.

Grid dome roofs have heretofore usually been embodied in a single course arrangement of arch-es. As such, a roof includes two series of parallel arches extending perpendicular to each other in the same spherical plane. These arches, normally I-beams, angle iron beams, or pipe beams, or the like, conventionally pass each other at double tenon cuts formed in each beam. The labor, time an expense which go into setting the perpendicular series of arches together in a single course grid is considerable.

In contrast to the single course structure, a double course grid dome is relatively simple to construct. No tenon cut or the like are required, for example. In addition, precise positioning of the crossed arches is not necessary to assembly. Nevertheless, the double course grid dome has not been popular because the disadvantages of its bulk and slightly greater weight have outweighed its advantages.

It is an object of the present invention to provide an improved selfsupporting roof structure of the grid dome type.

It is another object to provide an improved double course grid dome roof structure.

It is still another object to provide a double course grid dome roof structure which employs considerably less structural material, is correspondingly lighter, and yet is as strong and stable as prior art grid domes.

It is a further object to provide a grid dome roof in which grid arch spacing is made substantially greater than heretofore considered acceptable without a corresponding increase in the tendency of individual arches to buckle sideways in arch spans between tie points.

It is yet a further object to provide a grid dome roof structure which is relatively simple and inexpensive to construct.

It is still a further object to provide an improved method of constructing a double course grid dome.

The foregoing and other objects are realized in accord with the present invention by providing a grid dome roof structure which employs relatively fewer structural arches in a double course arrangement. The more widely spaced arches in the inner course are interconnected by relatively light intermediate members affixed to each inner arch at a predetermined position between bracketing arches of the outer course. In turn, the roof skin interconnects these intermediate members with the arches of the outer course by 'being affixed to each outer arch and intermediate member at a predetermined position between bracketing arches of the inner course. Cooperation between the intermediate members, the skin, and the arches in both the inner and outer courses through these interconnetcions is effective to increase the overall strength of the dome, reduce below prescribed limits the free tendency of arches to buckle sideways, and substantially lessen the overall weight of the dome.

A further aspect of the invention resides in the method of constructing a double course grid dome. It is simple and inexpensive, yet secures superior results in dome construction.

The invention, both as to it organization and method of operation, taken with further objects and advantages thereof, will best be understood by reference to the following description taken in connection with the accompanying drawings, in which:

FIGURE 1 is a side elevational view of a storage tank, with portions removed, having a grid dome roof structure (illustrated diagrammatically) embodying features of the present invention;

FIGURE 2 is a diagrammatic plan view of the grid dome roof structure illustrated in FIGURE 1, showing a portion of its skin;

FIGURE 3 is a sectional view taken through the actual structure of a grid dome roof embodying features of the present invention;

FIGURE 4 is an enlarged perspective view of the grid dome roof structure illustrated in FIGURE 3;

FIGURE 5 is a sectional view taken along line 55 of FIGURE 4; and

FIGURE 6 is a graphic illustration of formulae used in constructing a dome according to the present invention.

Pertinent to a concise definition and thorough understanding of the present invention, an explication of certain structural theroy and formulae, as well as their application to prior art grid domes, is in order. The first of such formulae defines the maximum load which a nonhinged, radially compressed circular arch will theoretically sustain before failure.

This load is expressed in pounds .per inch by the formula:

7 is a factor dependent upon the overall span of the arch,

E is the modulus of elasticity of the structural entity which defines the arch (in p.s.i.),

I is the moment of inertia of the arch (in inches R is the radius of the arch (in inches).

This formula is set out by Timoshenko in his book, Theory of Elastic Stability, 2nd edition, page 301. The formula is, of course, definitive of critical loading for a single arch. In a grid arrangement of arches, however, each arch adds to the strength of each other arch and the Q of an entire grid (per arch) is actually higher than the individually calculated Q for each arch. In fact, experience has taught that when the Timoshenko formula is applied to grid dome roof arches, a calculated critical load will inherently have a requisite safety factor of five plus.

To complicate the construction of grid domes, however, the arrangement of its arches is further limited by what is commonly known as the slenderness ratio of each arch span between its tie points. Although a grid may be of satisfactory strength under a radial load according to Timoshenko, its individual arches are susceptible to buckling failure (sideways) between tie points if their slenderness ratio is excessive. This slenderness ratio is a ratio of: the distance between stiffening tie points in an individual arch and the radius of gyration of the arch span between the tie points, written as l/r.

Certain trade organizations, such as the American Institute of Steel Construction, have set up building requirements which are defined in terms of the slenderness ratio, or l/r, for certain 'beam spans. To insure that the construction of grid type roofs in which the individual arches will not buckle sideways under load, a maximum l/ r of 120 has been adopted which corresponds to the values set by AISC for primary members at full compressive loads. The American Petroleum Institute also sets a maximum rafter span of five feet, six inches for the support of a thick tank roof (the maximum spacing, however, may vary depending on the type of covering being considered).

It will thus be apparent that there are three primary considerations in designing a grid dome for a tank roof or the like: (1) the vertical compression strength of the arch, (2) the maximum U1, and (3) the maximum arch spacing. Regarding the first, compression strength, a simplified graphic representation of the factors to be considered can be developed from Q. ='y El/R such as the formula:

S=Kl

where S is the maximum allowable arch spacing in feet for Q evaluated with a roof design load of thirty-five pounds per square feet (where 25 lb./ft. sq. is snow loading and 10 lb./ft. sq. is root skin weight) or Thus, the graph illustrated in FIGURE 6 can be drawn, giving a K factor for any selected roof radius within a given range.

Knowing the desired roof radius and the maximum arch spacing, the size of beam for the grid can be determined. It is then necessary only to determine whether the spacing and the radius or gy-ration of the beam provides an arch span slenderness ratio (l/ r) within allowable limits, since the Timoshenko formula does not take arch span lateral buckling tendencies into consideration.

An example of a grid dome constructed in accord with the prior art serves to better illustrate features of the present invention; the present invention taking the above values into consideration in generally providing an improved grid dome structure and more specifically an improved double course grid dome structure.

In the prior art, knowing from experience that an I-beam type structural member is necessary to obtain sufiicient strength in a relatively large tank roof, for example, with a maximum arch spacing of 5 6", a standard size unior I-beam (6 x 4 CB] 6) is necessary to satisfy the compressive load requirements for a dome of predetermined radius. This construction also affords an l/ r ratio of 77, which is well below the maximum of 120. A 120 diameter dome constructed in this manner would employ 4758 of 6 X 4 CB] 6 I-beam weighing 40,433 lbs.

In contrast, a double course grid dome construction embodying features of the present invention, when constructed in accordance with the size and load requirements for the exemplary prior art dome described above, results in a savings of 11,000 lbs. of structural steel. Furthermore, the present dome construction is as strong as the prior art dome while its l/r ratio is within the allowable range. Nevertheless, the time and expense of erectlng the present grid dome structure is substantially less than would 'be required for the prior art grid dome structure.

Referring now to the construction of a grid dome according to the present invention, and specifically to the drawings, a storage tank for petroleum products or the like is seen at 10 in FIGURE 1. The tank 10' includes a cylindrical body 11 which is 120 feet in diameter 1n the present instance. It is capped by a self-supporting grid dome roof embodying features of the present invention and illustrated generally at 12.

The roof 12 includes a large plurality of arches arranged in a grid pattern. The arches 15 have substantially identical radii of curvature corresponding to the radius of the sphere of which the dome roof 12 forms a part. In other words, each of the arches 15 in the dome roof 12 is constructed substantially on a great circle of this sphere.

The roof 12 is a double course grid dome wherein a first series 16 of the arches 15 lie generally parallel to each other and extend in one direction while a second series 17 of the arches overlie the first series, extending generally parallel to each other and perpendicular to the arches of the first series. As hereinafter discussed more specifically, the dome 12 is characterized by a predetermined relatively great spacing between the arches 15 in each series 16 and 17.

According to the present invention the series 16 and 17 of arches 15 are interconnected by and synergetically cooperate with light weight intermediate members 31 and the root skin 32. The intermediate members 31 are also arcnately formed substantially on the radius of the aforementioned great circle. The intermediate members 31 interconnect the arches 15 in the inner series 16 and are, in turn, interconnected with the arches 15 of the outer series 17 by the roof skin 32.

The intermediate members 31 exert a lateral tying effect on the arches 15 of the inner series 16, while the roof skin 32 exerts a lateral tying elfect on the arches 15 of the outer series 17. The total effect is to tie the entire matrix of arches 15 together with the connecting members 31 and the skin 32 so that they work together to stabilize the roof 12 and enhance its strength.

As a practical example of the grid dome construction embodying features of the present invention, attention is directed to FIGURES 3-5. Here it will be seen that each series 16 and 17 of arches 15 is composed of arcuately formed, generally parallel I-beams 40 (for ease of illustration, the I-beams 40 in FIGURE 4 are shown as being straight). Each I-bearn 40 is, in turn, composed of a suitable number of identical I-beam sections 41. Each of the arches 15 making up both series 16 and 17 of arches is assembled from straight I-beam sections 41 by merely butt welding the ends 42 of the I-beam sections together. Any excess length on a predetermined beam 40 is cut oil. in a suitable manner to precisely dimension each arch 15. The crossed I-beams 40 are tied together by welding or the like at 43.

In the dome roof 12 embodying features of the present invention, an 11 foot spacing is established between tie points 43 connecting the arches 15 in each of the series 16 and 17 of arches. Using the chart illustrated in FIG- URE 6 in the manner discussed relative to the exemplary prior art dome construction, it is thus determined that an 8 x 4 CB] 8 steel I-beam is required. This beam is twice as strong in a vertical cross section as the 6 x 4 CB] 6 I-beam used in the prior art grid dome because the spacing has been doubled.

With the larger beam 40 only 234-2 feet of beam is required, weighing a total of 23,420 lbs., because of the Wider arch 15 spacing. However, this arch 15 spacing arrangement gives a l/r ratio for each arch span between tie points 43 of approximately 161; substantially higher than the maximum of permitted. Use of the lighter intermediate members 31 and cooperating roof skin 32 according to the present invention reduces this l/r ratio to in the neighborhood of about 80.

The intermediate members 31 comprise relatively light weight angle irons 44 formed of standard length angle iron sections, welded together end-to-end. The angle irons 44 are considerably smaller than the I-beams 40, in keeping with their lighter weight, of course. As such they are tied to each arch 15 in the inner series 16 of arches by generally rectangular mounting plates 46 welded to the upper surface 47 of corresponding I-beams 40.

The depending legs 48 of the angle irons 44 are suitably welded or bolted to corresponding mounting plates 46 so that the members 31 interconnect the arches 15 of the inner series 16 and extend perpendicular thereto. An intermediate member 31 is spaced half way between each pair of parallel arches 15 in the outer series 17. Accordingly, the maximum unsupported length arch span in the inner series 16 between tie points 43 is approximately halved and the l/r ratio reduced to about 80. A total of 1208 feet of angle iron 44 is used, weighing 5920 lbs. Thus, the combination weight of beams 40 and intermediate members 31 is only 29,340 lbs. or a savings of 11,000 lbs.

The upper surfaces 51 of the horizontally disposed legs 52 on each angle iron 44 are co-planar with the spherical plane defined by the upper surfaces 53 on the outer series 17 of arches 15. As hereinafter described, these surfaces support the roof skin 32.

Erection and welding of the arches 15 and the intertermediate members 31 in the foregoing manner is preferably accomplished on the floor of the tank 12 within the confines of its body 11. With the arches 15 and the members 31 interconnected, the roof 12 (without its skin 32) is raised from the floor of the tank to a suitable level for attachment to a mounting ring (not shown) surmounting the tank body 11. The free ends of the arches are then appropriately connected to gusset plates (not shown) secured to the aforementioned ring by welding or the like.

With the interconnected arches 15 and intermediate members 31 suitably mounted in place on the tank body 11, sheets 60 of steel or the like are arranged over the connecting members 31 and arches 15- to form the skin 32. As illustrated, the sheets 60 are substantially rectangular and, the the present instance, are about 265 inches long and 90 inches wide. The sheets 60 are placed with their longitudinal axes parallel to the central arch 61 of the inner series 16 of arches 15, extending transversely across the intermediate members 31 and the arches 15 in the outer series 17. The sheets 60 preferably are Welded to the outer surfaces 53 and 51 of the outer series arches 17 and connecting members 31, respectively, at tie points 65 substantially half way between the parallel arches 15 in the inner series 16. The sheets 60 are preferably overlapped about one inch and welded together along their edges 66. Each sheet 60 is stiff enough to provide lateral tying support for the arches 15 in the outer series 17. The slenderness ratio of the arches 15 in the outer series 17 is thus reduced to about 80 also. In addition, the intermediate members 31 support the sheets 60 to prevent them from sagging between the arches 15.

The marked advantages of the present grid dome roof construction over prior art grid domes should now be readily apparent. First, the dome roof 12 embodying features of the present invention utilizes a double course arrangement of arches 15, facilitating simpler, less expensive, and more expeditious erection of a dome. Second, the requisite amount of structural steel beam material for a grid dome can be reduced by or thereabout; approximately 29,000 lbs. in the invention example as compared with approximately 40,000 lbs. in the corresponding exemplary prior art dome. This makes for great cost savings, of course. Third, the l/ r ratios for the arches 15 of the dome 12 are eminently satisfactory, even with relatively great spacing between arches.

While the embodiment described herein is at present considered to be preferred, it is understood that various modifications and improvements may be made therein, and it is intended to cover in the appended claims all such modifications and improvements as fall within the true spirit and scope of the invention.

What is claimed is:

1. A grid dome roof, comprising: an inner series of 6 curved arches, an outer series of curved arches extending perpendicular to said inner arches, said inner and outer arches being connected at main tie points where they cross, the length of the arch spans between said main tie points being such that the l/ r ratio of such arch spans exceeds a predetermined limit, roof skin overlying said outer arches and being connected to the outer surface of each outer arch, a series of relatively weak intermediate members overlying the arches of said inner series and extending between and substantially parallel to the arches of said outer series, said intermediate members being secured to said inner arches at first stiffening tie points where they cross each inner arch whereby the arch spans between tie points of said inner arches are shortened to the extent that the l/ r ratio for said inner arch spans is below said predetermined limit, the outer surfaces of said intermediate members being in substantially the same spherical plane as said outer arches, said roof skin being connected to the outer surfaces of said intermediate members and to the outer surfaces of said outer arches at second stiffening tie points between the arches of said inner series whereby the arch spans between tie points on said outer arches are shortened to the extent that the l/ r ratio for said outer arch spans is below said predetermined limit, said inner and outer arches being selected for their ability to sustain a predetermined load according to the formula:

QCRZ'YIEI/R3 where 71 is a factor dependent upon the overall span of the arch E is the modulus of elasticity of the structural entity which defines the arch (in p.s.i.)

I is the moment of inertia of the arch (in inches*) R is the radius of the arch (in inches) and the roof load Q is known.

2. The grid dome roof of claim 1 further characterized in that said inner and outer arches selected according to formula Q =v EI/R establish a load safety factor for said grid dome of at least five.

3. The grid dome roof of claim 1 further characterized in that said first and second stiifening tie points are each substantially half-way between bracketing main tie points.

4. The grid dome roof of claim 1 further characterized in that said predetermined limit l/ r ratio is at least as low as for said inner and outer arch spans with said intermediate members and roof skin secured in place.

5. The grid dome roof of claim 1 further characterized in that substantially all of the arches of both said inner series and said outer series of arches lie on great circle arcs of said roof.

6. In a grid dome roof including an inner series of segmentally circular arches of substantially identical radius of curvature, an outer series of segmentally circular arches extending perpendicular to and having substantially the same radius of curvature as said inner arches, said inner and outer arches being connected at main tie points where they cross, the length of the arch spans between said main tie points being such that the l/ r ratio of said arch spans exceeds a predetermined limit, roof skin overlying said outer arches and being connected to the outer surface of each outer arch, and said inner and outer arches being strong enough to support the design load for said roof, the improvement comprising: a series of relatively weak intermediate members overlying the arches of said inner series and extending between and substantially parallel to the arches of said outer series, said intermediate members being secured to said inner arches at first stiffening tie points Where they cross each inner arch whereby the arch spans between tie points of said inner arches are shortened to the extent that the l/r ratio for said inner arch spans is below said predetermined limit, the outer surfaces of said intermediate members being in substantially the same spherical plane as said outer arches, said roof skin being supported by said outer surfaces of said intermediate members to prevent said roof skin from sagging, said roof skin being connected to the outer surface of each outer arch at second stiffening tie points between the arches of said inner series whereby the arch spans between tie points on said outer arches are shortened to the extent that the l/ r ratio for said outer arch span is below said predetermined limit.

7. The improvement in grid dome roof of claim 6 further characterized in that said roof skin is secured to said outer surfaces of said intermediate members at tie points aligned with said second stiffening tie points.

8. The improvement in grid dome roof of claim 6 further characterized in that said first and second stifiening tie points are each substantially half-way between bracketing main tie points.

9. The improvement in grid dome roof of claim 8 further characterized in that said predetermined limit l/r ratio is at least as low as 120 for said inner and outer arch spans with said intermediate members and roof skin secured in place.

10. The improvement in grid dome roof of claim 9 further characterized in that said segmentally circular arches are comprised of relatively heavy structural beams, and said intermediate members are comprised of relatively light angle iron.

11. A method of constructing a double course grid dome comprising the steps of: erecting a substantially parallel inner series of arches formed of beams of predetermined size and strength, erecting a substantially parallel outer series of arches extending perpendicular to said inner arches and formed of substantially identical beams of predetermined size and strength, connecting said arches where they cross at tie points spaced a predetermined dis stance apart whereby the length of the arch spans between said tie points is such that the I/r ratio of said arches spans exceeds a predetermined limit, positioning relatively weak intermediate members on the arches of said inn-er series extending between and substantially parallel to the arches of said outer series, securing said intermediate members to said lower arches at first stitfening tie points where they cross each inner arch whereby the arch spans between tie points on said inner arches are shortened to the extent that the l/r ratio for said inner arches spans is below said predetermined limit, placing a roof skin over the outer surface of said intermediate members and the arches of said outer series, and securing said roof skin to the outer surface of each outer arch at second stiffening tie points between the arches of said inner series so that the arch spans between tie points on said outer arches are shortened to the extent that the 1/;- ratio for said outer arch spans is below said predetermined limit.

12. The method of claim 11 further characterized by and including the step of securing said roof skin to the outer surface of each intermediate member at tie points aligned with said second stiffening tie points.

13. The method of claim 11 further characterized by and including the step of: selecting said identical beams for said inner and outer arches according to the formula:

Qca=vi where 71 is a known factor dependent upon the overall span of the arch,

E is the modulus of elasticity of the structural entity which defines the arch (in p.s.i.),

I is the moment of inertia of the arch (in inches'*),

R is the known radius of the arch (in inches), and the roof load Q is known.

14. The method of claim 11 further characterized by and including the step of erecting substantially all of the arches of both said inner series and said outer series of arches on great circle arcs of said roof.

References Cited by the Examiner UNITED STATES PATENTS 35,630 6/1862 Rumbold 52-81 I 2,536,174 1/1951 Hamilton s2 s1 FOREIGN PATENTS 7 462,253 1/1950 Canada.

FRANK L. ABBOTT, Primary Examiner.

A. C. PERHAM, Assistant Examiner. 

1. A GRID DOME ROOF, COMPRISING: AN INNER SERIES OF CURVED ARCHES, AN OUTER SERIES OF CURVED ARCHES EXTENDING PERPENDICULAR TO SAID INNER ARCHES, SAID INNER AND OUTER ARCHES BEING CONNECTED AT MAIN TIE POINTS WHERE THEY CROSS, THE LENGTH OF THE ARCH SPANS BETWEEN SAID MAIN TIE POINTS BEING SUCH THAT THE L/R RATIO OF SUCH ARCH SPANS EXCEEDS A PREDETERMINED LIMIT, ROOF SKIN OVERLYING SAID OUTER ARCHES AND BEING CONNECTED TO THE OUTER SURFACE OF EACH OUTER ARCH, A SERIES OF RELATIVELY WEAK INTERMEDIATE MEMBERS OVERLYING THE ARCHES OF SAID INNER SERIES AND EXTENDING BETWEEN AND SUBSTANTIALLY PARALLEL TO THE ARCHES OF SAID OUTER SERIES, SAID INTERMEDIATE MEMBERS BEING SECURED TO SAID INNER ARCHES AT FIRST STIFFENING TIE POINTS WHERE THEY CROSS EACH INNER ARCH WHEREBY THE ARCH SPANS BETWEEN TIE POINTS OF SAID INNER ARCHES ARE SHORTENED TO THE EXTENT THAT THE L/R RATIO FOR SAID INNER ARCH SPANS IS BELOW SAID PREDETERMINED LIMIT, THE OUTER SURFACES OF SAID INTERMEDIATE MEMBERS BEING IN SUBSTANTIALLY THE SAME SPHERICAL PLANES AS SAID OUTER ARCHES, SAID ROOF SKIN BEING CONNECTED TO THE OUTER SURFACES OF SAID INTERMEDIATE MEMBERS AND TO THE OUTER SURFACES OF SAID OUTER ARCHES AT SECOND STIFFENING TIE POINTS BETWEEN THE ARCHES OF SAID INNER SERIES WHEREBY THE ARCH SPANS BETWEEN TIE POINTS ON SAID PUTER ARCHES ARE SHORTENED TO THE EXTENT THAT THE L/R RATIO FOR SAID OUTER ARCH SPANS IS BELOW SAID PREDETERMINED LIMIT, SAID INNER AND OUTER ARCHES BEING SELECTED FOR THEIR ABILITY TO SUSTAIN A PREDETERMINED LOAD ACCORDING TO THE FORMULA: 